A Poor Man's Derivation of Quantum Compass-Heisenberg Interaction: Superexchange Interaction in J-J Coupling Scheme

Abstract

The exchange interaction between 5d electrons in t${}_{2g}$ orbitals is derived in the J-J coupling scheme which is the appropriate basis in the case of strong spin-orbit interaction. From simple calculations, it is found that ferromagnetic Ising interaction (quantum compass model) occurs due to a selection rule of hybridization between ${\Gamma }_7$ and ${\Gamma }_8$ orbitals, while antiferromagnetic Heisenberg interaction appears from hybridization between ${\Gamma }_7$ orbitals. It is also found that the ferromagnetic Ising interaction becomes small as the spin-orbit interaction increases. Thus, the sign of exchange interaction changes from ferromagnetic Ising to antiferromagnetic Heisenberg interaction as the spin-orbit interaction increases.

arXiv comment5 pages, 5 figures, Accepted for publication in J. Phys. Soc. Jpn

References in corpus (5)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Effect of Spin-Orbit Interaction on (4d)^3- and (5d)^3 -Based Transition-Metal Oxides
• CaIrO3 post-perovskite, a j = 1/2 quasi-one-dimensional antiferromagnet

Cited by in corpus (8)

• Orbital effects in solids: basics, recent progress and opportunities
• Spin-orbital liquid state assisted by singlet-triplet excitation in $J=0$ ground state of Ba${}_3$ZnIr${}_2$O${}_9$
• Magnetism of Kitaev spin-liquid candidate material RuBr${}_3$
• Mechanism for subgap optical conductivity in honeycomb Kitaev materials
• Spin-orbit effects in pentavalent Iridates: Models and materials
• Electric-field control of magnetic anisotropies: applications to Kitaev spin liquids and topological spin textures
• Dzyaloshinskii-Moriya Interaction between Multipolar Moments in $5d^1$ Systems
• A $j_{\mathrm{eff}}=1/2$ pseudospinon continuum in CaIrO${}_3$